Peridynamic stress is a weighted static Virial stress

Abstract

The peridynamic stress tensor proposed by Lehoucq and Silling (2008) is cumbersome to implement in numerical computations. In this note, we show that the peridynamic stress tensor has the mathematical expression of a weighted static Virial stress derived by Irving and Kirkwood (1950), which offers a simple and clear expression for numerical calculations of peridynamic stress tensor.